EX Lup is a well-studied T Tauri star that represents the prototype of young eruptive stars EXors. In this paper we analyze new adaptive optics imaging and spectroscopic observations of EX Lup and its circumstellar environment in near-infrared in its quiescent phase. We observed EX Lup with the high contrast imager SPHERE/IRDIS in the dual-beam polarimetric imaging mode to resolve the circumstellar environment in near-infrared scattered light. We complemented these data with earlier SINFONI spectroscopy. We resolve for the first time in scattered light a compact feature around EX Lup azimuthally extending from 280deg to 360deg, and radially extending from 0.3arcsec to 0.55arcsec in the plane of the disk. We explore two different scenarios for the detected emission. One accounting for the emission as coming from the brightened walls of the cavity excavated by the outflow whose presence was suggested by ALMA observations in the J=3-2 line of 12CO. The other accounts for the emission as coming from an inclined disk. We detect for the first time a more extended circumstellar disk in scattered light, which shows that a region between 10 and 30 au is depleted of mum-size grains. We compare the J-, H- and K-band spectra obtained with SINFONI in quiescence with the spectra taken during the outburst, showing that all the emission lines were due to the episodic accretion event. Conclusions. Based on the morphology analysis we favour the scenario in which the scattered light is coming from a circumstellar disk rather than the outflow around EX Lup. We analyze the origin of the observed feature either as coming from a continuous circumstellar disk with a cavity, or from the illuminated wall of the outer disk or from a shadowed disk. Moreover, we discuss what is the origin of the mum-size grains depleted region, exploring the possibility that a sub-stellar companion may be the cause of it.
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